# Why use G-test and the likes for AB testing at all?

I am learning about AB testing using the G-test. In my example, I have a 2x2 contingency table.

>print(T)
response
AB    no yes Sum
A   29   7  36
B   23  16  39
Sum 52  23  75


Event A is the red background of a website. Event B is the blue background of a website. I showed the website to the total of 75 people. Yes is like, and no is the opposite. After running the G-test I get

>likelihood.test(T)

Log likelihood ratio (G-test) test of independence without
correction

data:  T
Log likelihood ratio statistic (G) = 4.1914, X-squared df = 1,
p-value = 0.04063


The p-value is pretty small (significant at the 5% level), so I reject the null that the samples A and B have the same performance. Now, I have two questions:

1. How do I know what background color is better and has the higher performance?
2. Why do I need the G test at all? I can just compare the percentage of likes for each background color. For red (A), 7/36=19.4%, and, for blue background (B), 16/39=41%. So, clearly B has the higher like percentage, hence, is better. So, why use G test at all?

Remark: I also use the Fisher exact test since one of the measured values, A_yes, is smaller than 10. The output is

> fisher.test(T)

Fisher's Exact Test for Count Data

data:  T
p-value = 0.04948
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
0.9167091 9.6380957
sample estimates:
odds ratio
2.841057


The p-value is nearly identical to the G-test's. So again why use the G-test or Fisher test at all when one can just compare the yes percentage for each event. Thanks.

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Which R packages' likelihood.test is this? The one in Deducer? –  Glen_b Jun 15 '14 at 4:16